You have $6$ reindeer, Prancer, Rudy, Balthazar, Quentin, Jebediah, and Lancer, and you want to have $3$ fly your sleigh. You always have your reindeer fly in a single-file line. How many different ways can you arrange your reindeer?
Solution: We can build our line of reindeer one by one: there are $3$ slots, and we have $6$ different reindeer we can put in the first slot. Once we fill the first slot, we only have $5$ reindeer left, so we only have $5$ choices for the second slot. So far, there are $6 \cdot 5 = 30$ unique choices we can make. We can continue in this way for the third reindeer, where we will have $4$ choices. So, the total number of unique choices we could make to get to an arrangement of reindeer is $6\cdot5\cdot4$. Another way of writing this is $\dfrac{6!}{(6-3)!} = 120$